If you're going to pay a shop to do it then you might be better off to just buy a new bike.
Shop rates are $60/hour or so, some higher, some lower. And if you're going full-boat on the bike then you'll be looking at new bearings or at least a major overhaul and regrease. Might as well throw in a frame corrosion preventative treatment once the bike comes back from the painters.
Getting the paint off the frame is an exercise in labor or money, you can sand or chemical strip it down yourself, or can pay to have it stripped. I don't think you'll find a bike shop that will strip the paint off for you, maybe, but probably not.
Rough guess is that you'll be looking at $300-$700 in parts and labor and paint charges if you have a LBS take care of the whole project for you.
Doing it yourself could be well under $300 and possibly under $100 depending upon how well you prep the frame and how fancy you want to get with the paint work.
I recently came across a Raleigh Marathon Another Raleigh Marathon :)
and decided it was a rider. I've got new tires on it now, re-wrapped the handlebars, got the shifting lubed up and adjusted, and it's a fairly good rider now. Not worth it to me to go farther with it, plus it's a little on a tall side for my legs, but it fits the stepson well so it will be a loaner for when he comes to visit and if I can get him interested in some longer rides.
Nice bikes, but not in the "collectable" category if I read right from searches on the site here. But if you do want to go full-boat with your's then my suggestion would be to do the work yourself as much as you can. And if you're going to repaint the frame then just use your LBS for the high cost tool items like removing and installing headset bearing cups and maybe the bottom bracket work. You might need a minor refacing on the bottom bracket to clean up extra paint and get a good surface, same on the headset, so taking a bare frame in to have that work done shouldn't be too bad if you go to the shop on a slow day and bring along a 12-pack of soda or something for the service guys.
Also, it might be good to just go talk to the service people, tell them what you want to do, and ask if there's anyone there who could walk you through the process and maybe help with the hard stuff in exchange for a little mentoring fee or a free lunch or three. I don't mean to shortchange the LBS, but sometimes on the "older" bikes a parallel path is sometimes better.
You might also hit some used book stores and find an older bicycle repair book. With a 1984 bike you don't need the most current service books, and you just might need something in that older book that has been dropped in more current books. For current books you might look at Zinn's roadbike repair book and the ParkTool School blue book. There are more expensive current options, but I'd personally use the money saved to buy some tools and a decent repair stand.
Other's might have differing opinions on this, and I don't mean to discourage you, but my strongest recommendation would be to do the work yourself. The knowledge you gain in the process will be worth it. Have patience, take your time, and keep it fun. And post a few pics of the bike if you can.